Science:Math Exam Resources/Courses/MATH110/April 2014/Question 03 (g)/Solution 1

We want to combine all of the information from the previous parts. One way we can visualise the information is to write the information over three number lines for $f(x)$, $f'(x)$, and $f''(x)$.

Using information from $f'(x)$ and $f''(x)$, we can sketch the shape of the graph in each section

Finally, we can join up the pieces and adjust the vertical shift so that it lines up with the information from $f(x)$.